Bayesian regression and classification using Gaussian process priors indexed by probability density functions

In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending Matérn family covariance functions. We use some tools from information geometry to improve efficiency and computational aspects Bayesian learning model. particularly show how a inference with process prior (covariance parameters estimation prediction) can be put into action on space Our framework has capacity classifiying infering data observations that lie nonlinear subspaces. Extensive experiments multiple synthetic, semi-synthetic real demonstrate effectiveness proposed methods in comparison current state-of-the-art methods.